A propeller shaft used in a power transmission system for a vehicle (such as an automotive vehicle) has been provided with universal joints and a slip joint. The propeller shaft is required to be free of unbalance during rotation. It has been proposed that such unbalance be corrected at a connecting member which is connected to a differential or a transmission, as disclosed in Japanese Utility Model Publication No. 6-65649. In this technique, an eccentric load generated through the connecting member in the propeller shaft is field-balanced in a stepless manner, in which means for adjusting balance of the propeller shaft is disposed at the flange section of the connecting member. Otherwise, it has been known that a balance weight for correcting unbalance of the propeller shaft be attached to the outer peripheral surface of the propeller shaft which has a slip joint, thereby reducing an unbalance force developed at the connecting members on engine power output and input sides.
However, where a propeller shaft is provided with a slip joint, including splines located between a sleeve shaft and a stub yoke or between a sleeve yoke and a stub shaft, an externally splined shaft is fitted in an internally splined sleeve so that a clearance is formed between the splines of the shaft and the splines of the sleeve. Under existence of this clearance, the splin shaft and the splined sleeve are allowed to radially move relative to each other, thereby changing the locational relative phase between the splined shaft and the splined sleeve. Accordingly, even if the balance adjusting means is provided at the flange section of the connecting member or the balance weight is attached to the outer peripheral surface of the propeller shaft, unbalance correction for the propeller shaft cannot be stabilized owing to the fact that the locational relative phase between the splined shaft and the splined sleeve is changeable. Making a fine correction of the unbalance has been particularly difficult. As a result, it is required to repeat unbalance correction and unbalance measurement. This not only increases the number of steps for unbalance correction but also provides a low reproducibility of the correction, so that only a method of correcting the unbalance in a trial and error manner has been unavoidably employed.